A multi-commodity location-inventory problem in a closed-loop supply chain with commercial product returns

Commercial product returns represent a growing financial and operational concern for many firms, and they consist of true and false failure returns in the real-world business. This paper studies a joint location-inventory problem in a closed-loop system by considering multi-commodity flows and commercial product returns. First, this problem is formulated as a mixed-integer nonlinear programming model. Next, a novel heuristic method based on differential evolution is designed to solve this model efficiently. Finally, numerical experiments and results are presented to validate the solution approach and provide meaningful managerial insights for business managers to improve their supply chain practice in a closed-loop system with false failure returns.